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On polynomial response surfaces and Kriging for use in structural optimization of crashworthiness
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
Linköping University, Department of Management and Engineering, Solid Mechanics. Linköping University, The Institute of Technology.
2005 (English)In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 29, no 3, 232-243 p.Article in journal (Refereed) Published
Abstract [en]

The accuracy of different approximating response surfaces is investigated. In the classical response surface methodology (CRSM) the true response function is usually replaced with a low-order polynomial. In Kriging the true response function is replaced with a low-order polynomial and an error correcting function. In this paper the error part of the approximating response surface is obtained from “simple point Kriging” theory. The combined polynomial and error correcting function will be addressed as a Kriging surface approximation.

To be able to use Kriging the spatial correlation or covariance must be known. In this paper the error is assumed to have a normal distribution and the covariance to depend only on one parameter. The maximum-likelihood method is used to find the latter parameter. A weighted least-square procedure is used to determine the trend before simple point Kriging is used for the error function. In CRSM the surface approximation is determined through an ordinary least-square fit. In both cases the D-optimality criterion has been used to distribute the design points.

From this investigation we have found that a low-ordered polynomial assumption should be made with the Kriging approach. We have also concluded that Kriging better than CRSM resolves abrupt changes in the response, e.g. due to buckling, contact or plastic deformation.

Place, publisher, year, edition, pages
2005. Vol. 29, no 3, 232-243 p.
Keyword [en]
Crashworthiness, FEM, Kriging RSM
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-45499DOI: 10.1007/s00158-004-0487-8OAI: oai:DiVA.org:liu-45499DiVA: diva2:266395
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13
In thesis
1. Structural optimization in vehicle crashworthiness design
Open this publication in new window or tab >>Structural optimization in vehicle crashworthiness design
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns the optimization of structures subjected to impact loading. Major applications can be found in the crashworthiness design of vehicles. There is an industrial interest in using optimization methods in the crashworthiness design process. However, strongly nonlinear responses, including high frequency components, make the Finite Element (FE) simulations computationally demanding. This fact restricts the number of possible optimization methods that can be applied.

In this work two optimization methods have been investigated: Response Surface Methodology (RSM) and Kriging. In both these methods the number of functional evaluations, i.e. here FE simulations, depends at least linearly on the number of design parameters. Thus, the number of design parameters is limited due to the computational effort. One objective of this work has been to reduce the total computational cost of the optimization process, or alternatively the possibility to use more design parameters at the same computational cost. When using RSM and Kriging, the number of functional evaluations in each iteration can be reduced, and/or the convergence of the optimization process can be improved. In many applications, RSM has been used with linear approximating response surfaces for robustness and efficiency reasons. Linear RSM may suffer from iterative oscillations, since the optimal design is often found on the boundary of the feasible design region. This oscillatory behaviour can be reduced if Kriging is used for the approximating response surfaces. However, it has been found that Kriging may have problems in fulfilling the constraints. In the initial design process of a structure very many alternative designs exist. At these early stages topology optimization is a mean of finding a structure that is optimal for the objective at hand. In this work a topology optimization approach is proposed for the design of crashworthiness structures. The resulting structure must still be subjected to an interpretation by engineers and also be improved by further optimization.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2005. 26 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 940
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-31403 (URN)17174 (Local ID)91-85297-78-X (ISBN)17174 (Archive number)17174 (OAI)
Public defence
2005-05-20, C3, C-huset, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2012-12-07Bibliographically approved

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Forsberg, JimmyNilsson, Larsgunnar

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